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Level crossings of a random trigonometric polynomial with dependent coefficients

Part of: Stochastic processes

Published online by Cambridge University Press:  09 April 2009

K. Farahmand
K. Farahmand
Affiliation:
Department of Mathematics, University of Ulster, Jordanstown, Co Antrim, BT37 OQB, United Kingdom
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Abstract

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This paper provides an asymptotic estimate for the expected number of K-level crossings of the random trigonometric polynomial g1 cos x + g2 cos 2x+ … + gn cos nx where gj (j = 1, 2, …, n) are dependent normally distributed random variables with mean zero and variance one. The two cases of ρjr, the correlation coeffiecient between the j-th and r-th coefficients, being either (i) constant, or (ii) ρ∣j−r∣ρ, j ≠ r, 0 < ρ < 1, are considered. It is shown that the previous result for ρjr = 0 still remains valid for both cases.

Keywords

number of real rootsKac-Rice formularandom trigonometric polynomial.

MSC classification

Secondary: 60G99: None of the above, but in this section
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 58 , Issue 1 , February 1995 , pp. 39 - 46
Copyright
Copyright © Australian Mathematical Society 1995

References

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